How to modify the form of an object?
You could do it with the Proportional Editing option on, but you should have a better result with the Mesh Deform modifier:


Create a cube that encompass your object.
Subdivide it a bit.
In the Properties panel > Data > Display, choose Maximum Draw Type > Wire so that it's transparent in Object mode. To make it transparent in Render mode, go in the Properties panel > Data > Cycles Settings and disable all.
Give your mesh a Mesh Deform modifier with the cube as Object. Click on the Bind button.
Move or scale the edges of your cube to modify the shape of your object.
When you're happy, apply the modifier (maybe keep a unapplied copy somewhere though).